Browsing by Author "Gath, Peter Friedrich"

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    CAMTOS - a software suite combining direct and indirect trajectory optimization methods
    (2002) Gath, Peter Friedrich; Well, Klaus Hinrich (Prof. Ph.D.)
    Many engineering applications involve the solution of optimal control problems. Such problems cover a wide variety of different disciplines, starting from typical aerospace applications, e.g. a fuel minimal launcher ascent trajectory, up to more exotic applications such as the optimal motion of the human body in different sport disciplines. This thesis presents a new method for solving a general class of multi-phase trajectory optimization problems. This new method uses a combination of direct multiple shooting and direct collocation. Depending on the specific demands of the problem to solve, a different kind of transcription method can be used for each phase. In addition, the method can be combined with the indirect method. Once the adjoint differential equations are available in addition to the dynamic system, one or more phases can be modeled as indirect phases. Since the transversality conditions that are usually required for solving the multi-point boundary value problem are contained in the Karush-Kuhn-Tucker conditions of the NLP-solver, they need not be formulated explicitly. The benefits of combining direct and indirect methods is demonstrated on an Ariane 5 dual payload mission. While the atmospheric parts of this mission are modelled with the direct multiple-shooting technique, the upper stage is using the indirect method. An analysis of the switching function, which is generated as a by-product of the indirect method, yields an improved mission profile. This profile involves an additional coast-arc and improves the pay-load performance by 66%. An additional example demonstrates the advantages of using direct collocation and direct multiple shooting to solve a complex branched trajectory optimization problem. The ascent and return of the suborbital Hopper vehicle is optimized such that the payload delivered to the geostationary transfer orbit by an upper stage is maximized. The robustness and large convergence radius of the direct collocation method significantly simplifies the generation of an approximate solution of the problem which is then refined by changing the transcription method of the atmospheric parts of the trajectory to the direct multiple shooting technique.